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Abstract.
Let 
be a domain. In 2007 Hencl, Koskela and Onninen proved that if 
is a homeomorphism of bounded variation then so does its inverse map 
. In this paper we present a different proof giving precise formulae for the total variations of the coordinate functions of 
, that is,
As an application, we prove that weak*-compactness in BV holds
simultaneously for sequences of BV-homeomorphisms fj and their
inverses 
; this symmetry result fails in the setting of
bi-Sobolev mappings. We also deduce by
the above formulae a slight generalization of a recent theorem of Iwaniec and
Onninen on the existence a.e. of a right inverse of weak limit of
-homeomorphisms. Extensions to higher dimension are given.
Received: 2011-12-19
Revised: 2012-06-29
Accepted: 2012-07-02
Published Online: 2013-07-01
Published in Print: 2013-07-01
© 2013 by Walter de Gruyter Berlin Boston
